Forward Invariance of Sets for Hybrid Dynamical Systems (Part II)

This article presents tools for the design of control laws inducing robust controlled forward invariance of a set for hybrid dynamical systems modeled as hybrid inclusions. A set has the robust controlled forward invariance property via a control law if every solution to the closed-loop system that...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2021-01, Vol.66 (1), p.89-104
Main Authors: Chai, Jun, Sanfelice, Ricardo G.
Format: Article
Language:English
Subjects:
Closed loop systems
Control design
Control theory
Discrete-time systems
Dynamical systems
Feedback control
Hybrid systems
Inclusions
Invariance
Liapunov functions
Lyapunov methods
nonlinear control systems
nonlinear dynamical systems
Robot arms
Robust control
robustness
Stability analysis
Thermal stability
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Summary:This article presents tools for the design of control laws inducing robust controlled forward invariance of a set for hybrid dynamical systems modeled as hybrid inclusions. A set has the robust controlled forward invariance property via a control law if every solution to the closed-loop system that starts from the set stays within the set for all future time, regardless of the value of the disturbances. Building on the first part of this article, which focuses on analysis, in this article, sufficient conditions for generic sets to enjoy such a property are proposed. To construct invariance inducing state-feedback laws, the notion of robust control Lyapunov function for forward invariance is defined. The proposed synthesis results rely on set-valued maps that include all admissible control inputs that keep closed-loop solutions within the set of interest. Results guaranteeing the existence of such state-feedback laws are also presented. Moreover, conditions for the design of continuous state-feedback laws with minimum point-wise norm are provided. Major results are illustrated throughout this article in a constrained bouncing ball system and a robotic manipulator application.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2020.2990665